In drilling boreholes for the purpose of retrieving mineral values which are deposited in relatively thin payzones, it is advantageous to be able to penetrate the payzone in a straight line, usually horizontally, or substantially horizontally, thereby exposing a generous area of the payzone to the borehole. Where the payzone may be located a few hundred feet below the surface of the ground, the borehole must deviate from the substantially vertical to a substantially horizontal path of penetration along a very sharp bend having a radius of curvature of the order of tens of feet, instead of a radius of curvature of thousands of feet common in conventional directional drilling.
In my previous patent application, Ser. No. 108,686; filed Dec. 31, 1979; now U.S. Pat. No. 4,333,539; and patent application Ser. No. 360,585; filed Mar. 22, 1982; now U.S. Pat. No. 4,432,423 as a divisional application of patent application, Ser. No. 108,686 to which reference is made for further background of the invention, there is disclosed both method and apparatus for carrying out drilling operations of this type. Reference is also made to the following issued patents which are related to the drilling of curved boreholes, i.e., curved boreholes having a high angle of deviation:
U.S. Pat. No. 2,699,920, Jan. 18, 1955 PA0 U.S. Pat. No. 2,708,099, May 10, 1955 PA0 U.S. Pat. No. 2,717,146, Sept. 6, 1955 PA0 U.S. Pat. No. 2,734,720, Feb. 14, 1956 PA0 U.S. Pat. No. 2,743,082, Apr. 24, 1956 PA0 U.S. Pat. No. 2,745,634, May 15, 1956 PA0 U.S. Pat. No. 2,745,635, May 15, 1956 PA0 U.S. Pat. No. 2,804,926, Sept. 3, 1957
A major drawback of the prior art of liquid (drilling mud) operated motors (or positive displacement motors) driving rock drill bit combinations lies in the diameter and length of the assembly being of a size which precludes the circumnavigation of a sharp bend. Consequently, the prior art of liquid operated turbine motors and bit assembly demands that a relatively long bend be made, which is undesirable as contrasted to a deviated hole which commences in a straight nearly vertical line for a few hundred feet in depth, and then abruptly deviates laterally through a high angle of curvature and penetrates the payzone substantially horizontally.
W. Tiraspolsky wrote a work entitled "The Theoretical Approach to Turbodrilling", published in World Oil, November and December 1957, in which he shows that downhole liquid operated turbine motors, also called turbodrills, produce power to actuate the shaft which rotates the rock bit with the kinetic energy of the fluid flowing through the motor.
The torque developed by a turbodrill is maximum when the turbodrill stalls. The stall torque T.sub.o is ##EQU1## where .eta.=Mechanical efficiency
n=Number of turbine stages PA1 w=Fluid density (lb/ft.sup.3) PA1 .epsilon.=Fluid loss coefficient PA1 Q=Fluid flow rate (ft.sup.3 /sec) PA1 g=Gravitational constant (32.2 ft/sec.sup.2) PA1 .lambda.=Fluid contraction coefficient PA1 b=Rotor vane width (ft) PA1 .beta.=Exit angle of rotor and stator blades. PA1 T=Torque (ft/lb). PA1 .eta.=0.85 PA1 w=74.9 lb/ft.sup.3 (10 lb/gal) PA1 .epsilon.=0 PA1 .lambda.=1 PA1 b=1/12 ft PA1 .beta.=45.degree. PA1 D=6/12 ft PA1 Length=2 nb.
The optimal power output of the turbodrill is proportional to the product of the speed N and the output torque T. This equation is ##EQU2## where N=Rotary speed (rpm)
The optimal power output is maximum at a speed equal to half the runaway speed as shown in the attached FIG. 1.
The turbodrill power output as a function of turbine rotary speed is shown in FIG. 2 and is given by: ##EQU3## where D=the normal rotor vane diameter (ft).
Using the above equations and various fluid flow rates, the length of the turbodrills to produce a nominal 20 HP shaft output are calculated in Table 1.
TABLE 1 ______________________________________ Q'(gal/min) Q(ft.sup.3 /sec) N.sub.R n Length (ft) ______________________________________ 200 0.45 262.7 1046 174.33 300 0.67 391.1 317 52.83 400 0.89 519.5 135 22.50 ______________________________________
where
In the above, a 7 in. diameter motor has been assumed (i.e., 6 in. diameter turbine blade). Considering the length of the turbine motor section above plus approximately 12 inches for the bit sub and bit, then the minimum radius of curvature of borehole that such a motor could circumnavigate would be the radii given in Table 2.
TABLE 2 ______________________________________ Q'(gal/min) Length (ft) .perspectiveto. Radius (ft) ______________________________________ 200 174.33 26,348.44 300 52.83 2,483.06 400 22.50 472.70 ______________________________________
It can be seen that a liquid operated turbodrill with a nominal 20 HP shaft output horsepower will have a length which precludes it from circumnavigating a sharp bend in the borehole, i.e., a bend with a radius of tens of feet.
In contrast, the downhole pneumatic turbine motor, havin a nominal 20 HP shaft output horsepower, will have a length of approximately two feet; this will allow it to circumnavigate a sharp bend in the borehole of a radius of the order of tens of feet.